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MANSW (The Mathematical Association of New South Wales, Inc) publishes past HSC paper books with solutions for all level maths.

Re: NSW to dump UAI! So am I still ranked against NSW students only or the whole of Australia as the name suggests?

lol i did mix it up..

I also don't know which area it's referring to just by looking at the answer. I'll have to try different possibilities(there are only two). I don't have time to do them now though.

Well, if exam papers don't state it clearly, just go with the simplest method. If the teacher insists it is wrong, then argue about the ambiguity of the question.

yea well, if a line is rotated, it will just be a shell with no volume (It just has a shape as it doesn't even have thickness) so V=0

If this is a volumes question as the title suggested, the question must be like "the region bound by the curve y=2cos2x and..... is rotated about the line x=pi/2"

so exactly which area is rotated?

\\y=sin^{-1}(sinx)=sin^{-1}f(x)$ which has domain restriction $-\frac{\pi}{2}\leq x\leq \frac{\pi}{2} \\y=sin(sin^{-1}x)=sinf(x)$ which does not have domain restriction.$ is what I think.

do you mean y=sin(arcsinx)?

It's different for different textbooks (even different questions in one textbook). In cases those textbooks make things unclear, bad luck.. Just guess or deduce from the answer... (Cambridge is the only book that clearly states what they want I think.) But exam questions should (not guarenteed)...

hmm i c.. thanks for reply

derivative of (x^2+2)=2x x/(x^2+2)=1/2*2x/(x^2+2) and now apply the formula, giving 1/2*ln(x^2+2)+c

What I thought was: Add more FeO (ignoring the "finely powdered" part). This increases the amount of FeO in the reaction vessel. However, FeO is just a solid. It is not going to vaporise or dissolve to a liquid for reaction. Hence FeO concentration remains the same whereas its amount increases...

When to use: when you see (derivative of denominator)/(denominator) inside an integral. What it is: y=log (to base e) x (I'll call it ln x) is an inverse function of y=e^x. Consider y=e^x change x and y x=e^y y=ln x. That's the definition of it. In graphical terms, it is a reflection of y=e^x on...

\\a=-kx+c=\frac{1}{2} \frac{dv^2}{dx} \\when x=0, a=-5, v=20 \\-5=c \\\therefore a=-kx-5 \\when x=12, a=-11 \\-11=-12k-5 \\-k=-\frac{1}{2} \\\therefore a=-\frac{1}{2}x-5 \\v^2=-\frac{1}{2}x^2-10x+c \\when x=0, a=-5, v=20 \\400=c \\\therefore v^2=-\frac{1}{2}x^2-10x+400 \\when v=0...

cause->therefore (or other words such as allows)->effect Then you've related cause to its effect.

The simplest way is to use many "therefore"s.. like -> Ethanol has non-polar ethyl group which exerts dispersion forces. THEREFORE it is soluble in non-polar substances. It also has a polar hydroxyl group, which exerts creates hydrogen bonding. This ALLOWS it to dissolve in polar substances as...

It's D. See below for brief explanation No, there is a distinction. Adding FeO does not affect the equilibrium since there is no change in concentration of any substance. FeO is a solid. Thus, my answer is D.

\\A=\pi r^2 \\\frac{dA}{dr}=2\pi r \\\therefore \frac{dA}{dr}\propto r